TL;DR: multiply the distance by a factor of 1.4x for every stop of ISO over 100 you're using, similar to a full stop on the f-number scale over f/1. (e.g., if you're +3EV at iso 800, multiply by 2.8x).

First off, there are easier flashes to use with an FM than a YN-560IV. A vintage Nikon SB-26, would have an A(uto) mode on it that would use a sensor on the flash to determine the correct power cut-off automatically. It was the old-style way of automating flash power before TTL. And it would also have a distance scale on its LCD that does all the guide number calculations for you if you set the iso and aperture you're using.

Secondly, your FM's flash sync speed is 1/125s. You cannot use a faster shutter speed than that with flash and avoid banding, because either/both of the shutter curtains will be covering part of the frame while the flash burst goes off.

The basic guide number math that that table is giving you is that:

distance light can travel = GN / f-number

(for ISO 100, and a given zoom setting). The zoom setting adjusts how focused the beam is for angular coverage by shifting the bulb in the head forwards and back. The higher the zoom (in mm), the more narrowly focused and stronger the beam will be. So it does affect the light output as well. The YN-560 IV's GN spec. is 58m/190' at iso 100, zoomed to 105mm.

For every stop your ISO increases, you can multiply the GN (and thus the distance) by a factor of 1.4x (square root of 2).

ISO = Factor x

• 100 = 1
• 200 = 1.41
• 400 = 2
• 800 = 2.83
• 1600 = 4
• 3200 = 5.66
• 6400 = 8

See also: scantips.com's "Understanding Guide Numbers" article.

But. These GN calculations only work for bare, direct flash pointed straight forward. If you're going to bounce the flash, or use the flash off-camera behind a modifier, these GN calculations may no longer be accurate.

Which was why, back in film days, flash photographers used incident handheld flash meters (all flash meters are light meters; not all light meters are capable of measuring flash). The meter is held in front of the subject, the flash is fired at a given power level, and the meter is set for a specific iso and the meter tells you the aperture that would give you good exposure for that power setting. Or you shot test polaroids to get fast feedback. Maybe both.

Last but not least, learning flash requires a lot of trial and error. That can get very expensive and time-consuming (because you have to keep track of what you did on which frame as well as because you're working blind and on a time delay) with film. It may make sense to get yourself a cheap digital camera with a flash hotshoe (even a P&S fixed-lens camera) to try and sort out the basics of how flash works without paying for lots of film, developing, and scanning/printing along the way. It is incredibly easy to ruin an entire roll without any clue as to what you did wrong with a flash. And with digital, the instant feedback and re-shoot capability can really speed up learning.

See also:

• The Strobist Lighting 101. It's about off-camera flash, but also teaches a manual flash workflow.
• Tangents "Flash Photography Techniques" which is about TTL on-camera bounce flash, but can still get you through a lot of the basics of flash exposure and flash/ambient balance and also teaches on-camera bounce flash.